Question

Many early chemists noted a diagonal relationship among elements in the periodic table, whereby a given element is sometimes more similar to the element below and to the right than it is to the element directly below. Lithium is more similar to magnesium than to sodium, for example, and boron is more similar to silicon than to aluminum. Use your knowledge about the periodic trends of such properties as atomic radii and \(Z_{\text {eff }}\) to explain the existence of diagonal relationships.

Short answer

Diagonal relationships arise due to similar atomic radii and effective nuclear charge.

Step-by-step solution

Understanding Diagonal Relationships

Diagonal relationships in the periodic table occur when an element in the second period shows similarities with an element in the third period, which is one group to the right. This happens because certain chemical properties progressively change across a period and down a group, allowing some similarities to arise diagonally across the table.

Analyzing Atomic Radii

Atomic radii decrease across a period from left to right due to increasing nuclear charge which pulls electrons closer to the nucleus, and increase down a group as additional electron shells are filled. Consequently, elements that are diagonally related have radii that are more similar when compared with elements that are directly below or to the right.

Considering Effective Nuclear Charge \\((Z_{eff})\\)

Effective nuclear charge \(Z_{eff}\) increases across a period as electrons are added to the same energy level while protons are added to the nucleus, causing valence electrons to experience a stronger pull towards the nucleus. Diagonally related elements can have a similar \(Z_{eff}\) as this balance of charge impacts properties such as ionization energy and electronegativity similarly.

Applying to Lithium and Magnesium

Lithium (Li) is smaller and has a higher \(Z_{eff}\) relative to sodium (Na), making it more similar to magnesium (Mg) which also balances a smaller atomic size and high \(Z_{eff}\). Consequently, the chemical reactivity of Li and Mg can be more comparable than that of Li and Na.

Applying to Boron and Silicon

Boron (B) and silicon (Si) share similarities due to having comparable \(Z_{eff}\) and atomic radii, despite being from different periods and groups. In contrast, aluminum (Al) has a significantly larger atomic radius and lower \(Z_{eff}\) compared to B, making B more similar to Si in terms of chemical properties like metalloid characteristics.

Key concepts

Periodic Trends

The periodic table is a fascinating guide to understanding trends in chemical behavior. These trends include variations in properties like atomic radii, ionization energy, and electronegativity.
As you move across a period from left to right, the nuclear charge, or the number of protons, increases in the elements. This causes changes in several atomic properties.
From top to bottom in a group, there is an increase in atomic radius due to the addition of a new electron shell with each subsequent element.
Interestingly, diagonal relationships illustrate that an element can share properties with another element that is both in the next period and in a group to the right.

• For example, lithium and magnesium show similarities despite being in different periods and groups.
• This occurs because the cumulative periodic trends foster a balance of atomic characteristics.

Atomic Radii

Atomic radius refers to the size of an atom, measured from the nucleus to the outermost electron shell.
As you proceed across a period from left to right, atoms become smaller. This is due to increased protons in the nucleus, which pull electrons closer, reducing the atomic size.
Conversely, moving down a group, the atomic radius increases. This happens because additional electron shells are added, pushing the outermost electrons further from the nucleus.

• In the context of diagonal relationships, the atomic radii of elements like lithium and magnesium seem more similar than lithium and sodium, even though sodium is directly below lithium.
• This is due to the balance struck by the opposing effects of increasing nuclear charge and additional electron shells.

Effective Nuclear Charge (Z_eff)

Effective nuclear charge ( Z_{eff} ) describes the net positive charge experienced by electrons in an atom.
It takes into account the actual nuclear charge, less the shielding effect from the inner electrons. As a result, Z_{eff} increases across a period because added valence electrons do not shield each other effectively against the increasing nuclear charge.
This elevated Z_{eff} causes electrons to be held more tightly to the nucleus, influencing properties like ionization energy and reactivity.

• Elements with diagonal relationships, such as boron and silicon, might share similar Z_{eff} . This is why they show similarities despite differences in their groups and periods.
• In contrast, boron and aluminum differ more in their chemical behavior due to larger disparities in their Z_{eff} and atomic radii, illustrating the concept of periodic trends fueling diagonal relationships.